We explain how using the Floer version of persistence homology, we can find invariants of Rokhlin equivalence classes i.e. $f \simeq g$ if there is a chain $f_0=f,.... f_n=g$ such that the $C^0$ closure of the conjugacy orbit of $f_i$ and $f_{i+1}$ meet. We shall explain the $2$ dimensional case, and its generalization to higher dimensions using the $C^0$ continuity of γ explained in Sobhan's talk.